# US 7,609,749 B1 · Method and apparatus for generating non-recursive variable rate orthogonal spreading codes

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- Number: US 7,609,749 B1
- Document ID: US7609749B1
- Status: Granted
- Kind: B1
- Application number: 12/080,131
- Filed: 2008-03-31
- Granted: 2009-10-27
- Earliest claimed: 2003-07-17
- Assignees: L-3 Communications Corporation
- Inventors: Eric K. Hall; Thomas R. Giallorenzi; Richard B. Ertel
- Web page: https://patentgrep.com/patent/US7609749B1

## CPC

- H04J 13/0044: {OVSF [orthogonal variable spreading factor]}
- H04J 13/12: Generation of orthogonal codes
- H04J: MULTIPLEX COMMUNICATION (transmission in general H04B; peculiar to transmission of digital information H04L5/00; systems for the simultaneous or sequential transmission of more than one television signal H04N7/08; in exchanges H04Q11/00; stereophonic systems H04S)

## Abstract

A method for constructing and selecting non-recursive orthogonal variable spreading factor (OVSF) codes is provided. The method includes: defining a variable B=SFmax/SFmin, where SFmax is a maximum desired spreading factor and SFmin is a minimum desired spreading factor; forming B unique base matrices Gk of dimension SFmin×SFmin, where GiGiT=SFminImin ∀i, where T denotes a matrix transpose and Imin is an SFmin×SFmin identity matrix; forming a modulation matrix M of dimension B×B such that MMT=BIB, where IB is a B×B identity matrix; forming an SFmax×SFmax orthogonal variable spread factor (OVSF) code matrix C′ as: C ′ = [ M 1 , 1 · G 1 M 1 , 2 · G 2 … M 1 , B · G B M 2 , 1 · G 1 M 2 , 2 · G 2 … M 2 , B · G B ⋮ ⋮ ⋰ ⋮ M B , 1 · G 1 M B , 2 · G 2 … M B , B · G B ] , where Mi,j is a scalar from the i-th row and j-th column of the modulation matrix M, Gl . . . GB is the k-th base matrix Gk and Mi,j·Gk denotes the multiplication of the elements of Gk by the scalar Mi,j; selecting a row of the OVSF code matrix C′ to use as a pseudo-noise (PN) code; and one of spreading or despreading a signal using the selected PN code.

## Claims

### Claim 1

A method comprising:
defining a variable B=SFmax/SFmin, where SFmax is a maximum desired spreading factor and SFmin is a minimum desired spreading factor, where SFmax and SFmin are integer values;
forming B unique base matrices Gk of dimension SFmin×SFmin, where GiGiT=SFminImin ∀i, where T denotes a matrix transpose and Imin is an SFmin×SFmin identity matrix;
forming a modulation matrix M of dimension B×B such that MMT=BIB, where IB is a B×B identity matrix;
forming an SFmax×SFmax orthogonal variable spread factor (OVSF) code matrix C′ as:
C
′
=
[
M
1
,
1
·
G
1
M
1
,
2
·
G
2
…
M
1
,
B
·
G
B
M
2
,
1
·
G
1
M
2
,
2
·
G
2
…
M
2
,
B
·
G
B
⋮
⋮
⋰
⋮
M
B
,
1
·
G
1
M
B
,
2
·
G
2
…
M
B
,
B
·
G
B
]
,
where Mi,j is a scalar from the i-th row and j-th column of the modulation matrix M, Gl . . . GB is the k-th base matrix Gk and Mi,j·Gk denotes the multiplication of the elements of Gk by the scalar Mi,j, where i, j and k are integer values;
selecting a row of the OVSF code matrix C′ to use as a pseudo-noise (PN) code; and
one of spreading or despreading a signal using the selected PN code, where the steps of defining, forming the B unique base matrices, forming the modulation matrix M, forming the OVSF code matrix C′, selecting and one of spreading or despreading are performed by at least one processor.

### Claim 2 (depends on 1)

The method as in claim 1, where SFmax and SFmin are measured in chips per modulated symbol.

### Claim 3 (depends on 1)

The method as in claim 1, further comprising: performing at least one constrained column-wise permutation on the OVSF code matrix C′ prior to selection of the row, where the constraint on the at least one constrained column-wise permutation is designed to preserve OVSF properties of the permuted code matrix C′.

### Claim 4 (depends on 1)

The method as in claim 1, where the B unique base matrices Gk comprise Hadamard matrices.

### Claim 5 (depends on 1)

The method as in claim 1, where the method is implemented within a multi-rate code division multiple access (CDMA) wireless communication system.

### Claim 6 (depends on 5)

The method as in claim 5, wherein the multi-rate CDMA wireless communication system comprises at least one fixed subscriber unit or at least one mobile subscriber unit.

### Claim 7

An apparatus comprising:
at least one processor configured to define a variable B=SFmax/SFmin, where SFmax is a maximum desired spreading factor and SFmin is a minimum desired spreading factor and where SFmax and SFmin are integer values; to form B unique base matrices Gk of dimension SFmin×SFmin, where GiGiT=SFminImin ∀i, where T denotes a matrix transpose and Imin is an SFmin×SFmin identity matrix; to form a modulation matrix M of dimension B×B such that MMT=BIB, where IB is a B×B identity matrix; to form an SFmax×SFmax orthogonal variable spread factor (OVSF) code matrix C′ as:
C
′
=
[
M
1
,
1
·
G
1
M
1
,
2
·
G
2
…
M
1
,
B
·
G
B
M
2
,
1
·
G
1
M
2
,
2
·
G
2
…
M
2
,
B
·
G
B
⋮
⋮
⋰
⋮
M
B
,
1
·
G
1
M
B
,
2
·
G
2
…
M
B
,
B
·
G
B
]
,
where Mi,j is a scalar from the i-th row and j-th column of the modulation matrix M, Gl . . . GB is the k-th base matrix Gk and Mi,j·Gk denotes the multiplication of the elements of Gk by the scalar Mi,j, where i, j and k are integer values; and to select a row of the OVSF code matrix C′ to use as a pseudo-noise (PN) code; and
a transceiver configured to transmit or receive a signal using the selected PN code.

### Claim 8 (depends on 7)

The apparatus as in claim 7, where SFmax and SFmin are measured in chips per modulated symbol.

### Claim 9 (depends on 7)

The apparatus as in claim 7, where the at least one processor is further configured to perform at least one constrained column-wise permutation on the OVSF code matrix C′ prior to selection of the row, where the constraint on the at least one constrained column-wise permutation is designed to preserve OVSF properties of the permuted code matrix C′.

### Claim 10 (depends on 7)

The apparatus as in claim 7, where the B unique base matrices Gk comprise Hadamard matrices.

### Claim 11 (depends on 7)

The apparatus as in claim 7, where the apparatus comprises a unit within a multi-rate code division multiple access (CDMA) wireless communication system.

### Claim 12 (depends on 11)

The apparatus as in claim 11, where the apparatus comprises a fixed subscriber unit or a mobile subscriber unit.

### Claim 13 (depends on 7)

The apparatus as in claim 7, where the apparatus comprises a subscriber unit.

### Claim 14 (depends on 7)

The apparatus as in claim 7, wherein the apparatus comprises a base station.